The DirectSearchpackage is a collection of commands to numerically compute local and global minimums (maximums) of nonlinear multivariate function with (without) constraints. The package optimization methods are universal derivative-free direct searching methods, i.e. they do not require the objective function and constraints to be differentiable and continuous.

The package also contains commands for multiobjective optimization, solving system of equations, fitting nonlinear function to data by various methods.

The package optimization methods have quadratic convergence for quadratic functions.

The following is a summary of the major improvements in DirectSearch v.2.

-- Three new derivative-free optimization methods (Powell’s, Brent’s, and successive quadratic approximation) are added. Now Search command has four methods: cdos (conjugate direction with orthogonal shift), powell, brent, and quadratic. All four methods have quadratic convergence for quadratic functions.

-- The new global optimization command GlobalOptima is added.

-- The commands for multiobjective optimization, solving system of equations, fitting nonlinear function to data are added.

-- Mixed integer-discrete-continuous optimization is now supported.

-- You can now specify inequality constraints as any Boolean expressions.

-- You can now set bound inequality constraints x>=a, x<=b as: x=a..b.

-- Assume and assumption commands are supported for inequality constraints.

-- You can now specify problem variables as Vector.

-- High dimensional optimization problem are now solved a much faster.